Style: The class is interactive. Students may ask questions at any time, the instructor will explain and will not move on unless everyone is ready. The class is designed to help with the majority of standardized tests, including the SAT, which means we will go into details and types of questions that may be somewhat different from school assignments. In general, we do not promote learning by rote and we do not assign 'busy homework'. This class is harder and more detailed than the usual school class - the student must be willing to take on a challenge! Our class is close in difficulty and style to what is currently taught in Eastern Europe, Russia and some Western European countries.

Credit: There is no credit for this class. Our goal is to help students understand logically, memorize for the long term and enjoy the control they acquire over the subject matter. We believe there is a conflict of interest between selling knowledge and selling credits, therefore we do not grade students' performance and we do not give credit. For parents' information, we send a progress report based on classroom observations and homework completion.

Set Theory: definitions, operations, introduction to sets of numbers.

Functions: definition, domain, range, graph, monotony, onto, one-to-one, bijective, invertible, equations, roots, asymptotes, symmetry, parity.

Linear Systems: graphic interpretation, solutions, classification, matrices, operations with matrices, determinants, Cramer's rule, Gaussian elimination.

Power and Radical Functions: definitions, graphing power functions, properties, inverses, radical functions, domain and range.

Polynomials I: definition, operations, Euclid's algorithm, roots, fundamental theorem of algebra. application to quadratics.

Quadratic Functions: graph, symmetry, transformations, analysis, real and complex roots, Viete's relations, parabolas with parameters.

Complex Numbers: definition, operations with complex numbers in algebraic form.

Polynomials II: real roots, real coefficients, complex roots, integer coefficients, rational root theorem, Descartes' rule of signs, Viete's relations, graphing.

Rational Functions: definition, domain and range, asymptotes.

Exponential and Logarithmic Functions: definitions, domain, range, graph, monotony, properties, equations, applications to exponential growth and decay processes.

Algebraic Identities: more advanced algebraic identities and their uses in problem solving.

Absolute Value Functions: absolute value functions and graphs.

Sequences and Series: arithmetic, geometric, combinations thereof.

Combinatorics, Probability and Statistics: binomial theorem, permutations, combinations, sum and product rule, conditional probability, statistics definitions, standard deviation, binomial distributions, normal distributions.

Analytic Geometry: parabolas, ellipses, hyperbolas.

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We send GOTM lecture notes and homework at each lesson. Answer keys and full solutions are sent before the next lesson.